Optical Imaging and Scanning of Holes

ABSTRACT

Methods and apparatus for optical imaging and scanning of holes machined, drilled or otherwise formed in a substrate made of composite or metallic material. The method utilizes an optical instrument for imaging and scanning a hole in combination with an image processor configured (e.g., programmed) to post-process the image data to generate one complete planarized image without conical optical distortion. The optical instrument includes an optical microscope with confocal illumination and a conical mirror axially positioned to produce a full 360-degree sub-image with conical distortion. In the post-processing step, a mathematical transformation in the form of computer-executable code is used to transform the raw conical sub-images to planar sub-images. The planarized sub-images may be stitched together to form a complete planarized image of the hole.

BACKGROUND

This disclosure generally relates to methods and apparatus forinspecting holes machined in a workpiece or structure and, in particularrelates to methods and apparatus for inspecting holes designed toreceive fasteners.

Lightweight composite materials (such as fiber-reinforced plasticmaterial) are being used more extensively in the aerospace industry forboth commercial and military aircraft and other aerospace vehicles, aswell as in other industries. The structures using these compositematerials may be formed using multiple plies or layers of material thatmay be laminated together to form high-strength structure. At least onemethod for fastening multiple layers of material together is to clamp upthe layers, drill holes, and then insert some type of fastener into theholes and thereby secure the layers together.

In the field of manufacturing, frequent measurement and inspection areundertaken to ensure that manufactured parts conform to designspecifications. This includes the inspection of holes, such as drilledholes, to ensure that the holes are of the desired shape andconfiguration, e.g. diameter and alignment, within engineeringtolerances. Ensuring conformance of production parts to designspecifications is of particular concern in industries such as aerospacemanufacturing, where exacting production standards are maintained.

To ensure compliance of drilled holes with their design specifications,it has generally been the practice either to have a quality control orquality assurance inspector examine each hole, or to use statisticaltechniques to analyze a sampled number of holes. Inspection may beperformed by manually inserting a hole diameter probe, such as acapacitance-based probe, an air pressure hole probe, a laser hole probe,or a ball-type probe, into a hole to check its compliance with orvariation from design specifications. One technique for optical imagingof composite or metallic holes can only acquire shallow-depth images atoffset angles with respect to the hole center line (hereinafter, the“Z-axis”) due to the very narrow field-of-view of standard microscopesalong an optical axis (which is the same as the Z-axis of the hole).Such optical imaging is also unable to produce a full 360-degree planarimage of a hole in a single focal plane.

It would be advantageous to provide an apparatus that can scan along theZ-axis inside holes in a structure to assess the condition of the hole.

SUMMARY

The subject matter disclosed in detail below is directed to methods andapparatus for optical imaging and scanning of holes machined, drilled orotherwise formed in a substrate made of composite or metallic material.The method described herein utilizes an optical instrument for imagingand scanning a hole in combination with an image processor configured(e.g., programmed) to post-process the image data to generate onecomplete planarized image without conical optical distortion. Inaccordance with some embodiments, the optical instrument includes anoptical microscope with confocal illumination and a conical mirroraxially positioned to produce a full 360-degree sub-image with conicaldistortion. In the post-processing step, a mathematical transformationin the form of computer-executable code is used to transform the rawconical sub-images to planar sub-images. The planarization of thesub-images is done using a simple mathematical transformation of imagebits. The planarized sub-images may be stitched together to form acomplete planarized image of the hole.

By design, microscopes use lenses and/or mirrors to focus light onto animage sensor such as a focal plane array of opto-electrical elementsthat convert impinging light to electrical signals (hereinafter “arrayof photodetectors”) that represent pixel data of an image. As usedherein, the term “photodetector” means a device that is capable ofemitting electrons in response to photons impinging on a surface of thedevice. The apparatus includes a 90-degree “conical mirror” installed ona moving stage that is movable in a direction parallel to Z-axis of thehole while the axis of the cone is co-axial with the Z-axis of the hole.It should be appreciated, however, that a truncated conical mirror(a.k.a. “frusto-conical mirror”) may also be used. A mirror having areflective surface that is either conical or frusto-conical will bereferred to herein as a “conical mirror”.

The subject matter disclosed in detail below is further directed to anautomated high-speed method for inspecting holes in structures to befastened and a computer-controlled apparatus for performing thatinspection method. In accordance with various embodiments, the apparatuscomprises a multi-motion inspection head mounted on a scanning bridge,an end of a robotic arm, or a robotic crawler vehicle. The multi-motioninspection head comprises the aforementioned optical instrument and amotorized multi-stage probe placement head that is operable fordisplacing the optical instrument along X, Y and Z axes to achievemultiple sequenced motions. The optical instrument is attached to amandrel that is rotatably coupled to an X-axis (or Y-axis) stage forrotation about the Z axis. Smart servo or stepper motors with feedbackcontrol are used to move the optical instrument into place and then scaninside each hole in succession. In accordance with one embodiment, theapparatus comprises various directional motorized stages that aresequenced and controlled for the specific motions needed to inspect rowsof holes.

In accordance with some embodiments, the microscope and light source ofthe optical instrument are contained within a housing that is carried bythe multi-motion inspection head. The optical instrument furtherincludes an optical probe (e.g., a conical mirror and associated supportstructure) that extends downward from the housing. The optical probe issized and shaped to fit inside a hole to be inspected. The multi-motioninspection head is configured to move the microscope until the opticalaxis of the optical probe is aligned with the center line (Z-axis) ofthe hole and then insert the probe into the hole until the optical probeis at a starting depth inside the hole. The image sensor of themicroscope then acquires sub-images of the interior surface of the holeat different depths. In accordance with one proposed implementation, themulti-motion inspection head moves the optical probe along the Z-axis ofthe hole intermittently and the image sensor acquires raw conicalsub-images in the time intervals during which the optical probe isstationary. After one hole has been fully inspected, the optical probeis removed from that hole and then inserted into the next hole to beinspected. In this manner, a multiplicity of holes in a row of holes maybe inspected in succession.

In accordance with some embodiments, light from a light source isdirected axially (or nearly axially) into the hole during imageacquisition. Axially propagating light is directed radially outwardtoward a confronting portion of the hole. This radial re-direction ofthe illumination light is achieved using a conical mirror. The conicalmirror has a conical (or frusto-conical) surface, the apex of which isdisposed along the optical axis of the microscope. The conical mirrorreceives axially (or nearly axially) propagating light from the lightsource and reflects the light radially outward to illuminate aconfronting 360-degree portion of the hole in which the optical probe isinserted.

The method proposed herein provides a simple yet thorough opticalinspection. Also hole surface roughness and hole diameter variation canbe assessed fully in a single scan. Instead of providing only localinformation within the probe's curvature radius, the optical inspectiontechnique disclosed herein produces a full 360-degree view.

Although various embodiments of methods and apparatus for opticalimaging and scanning of holes are described in some detail later herein,one or more of those embodiments may be characterized by one or more ofthe following aspects.

One aspect of the subject matter disclosed in detail below is an imagingdevice comprising: a housing; a light source disposed inside thehousing; an image sensor disposed inside the housing; a conical mirrordisposed outside the housing and having a cone axis; a conical mirrorsupport structure that supports the conical mirror in a fixed positionrelative to the housing; and an optical subassembly supported by thehousing and configured so that light from the light source impinges onthe conical mirror and is reflected radially outward by the conicalmirror and light propagating radially inward and impinging on theconical mirror is directed onto the image sensor.

In accordance with some embodiments of the optical instrument describedin the immediately preceding paragraph, the conical mirror supportstructure comprises a central post; and the conical mirror is truncatedand attached to one end of the central post. In accordance with otherembodiments, the conical mirror support structure comprises a circularcylindrical glass tube having a cylinder axis; and the conical mirror isdisposed inside the circular cylindrical glass tube so that the coneaxis is coaxial with the cylinder axis.

Another aspect of the subject matter disclosed in detail below is amethod for imaging a hole in a substrate, the method comprising: (a)placing a conical mirror into a hole with a cone axis coaxial with ahole center line and with an apex or truncated portion of the conicalmirror at a first depth which is less than a second depth of a base ofthe conical mirror; (b) illuminating the conical mirror with light thatis focused onto a focal plane inside the hole; (c) reflecting the lightrecited in step (b) radially outward toward the hole using the conicalmirror; (d) reflecting returning light axially upward toward the openingusing the conical mirror; (e) directing light reflected axially upwardby the conical mirror in step (d) onto an image sensor; and (f)converting light that impinges on the image sensor into electricalsignals that represent pixel data of a first distorted sub-image of afirst portion of the hole having conical optical distortion. The methodfurther comprises processing the pixel data of the first distortedsub-image to produce pixel data representing a first planarizedsub-image without conical optical distortion.

The method described in the immediately preceding paragraph may furthercomprise: (g) moving the conical mirror along the hole center line to aposition where the apex or truncated portion of the conical mirror is ata third depth which is closer to the second depth than to the firstdepth; (h) illuminating the conical mirror with light that is focusedonto the focal plane inside the hole; (i) reflecting the light recitedin step (h) radially outward toward the hole using the conical mirror;(j) reflecting returning light of the light recited in step (i) axiallyupward toward the opening using the conical mirror; (k) directing lightreflected axially upward by the conical mirror in step (j) onto an imagesensor; and (I) converting light that impinges on the image sensor intoelectrical signals that represent pixel data of a second distortedsub-image of a second portion of the hole having conical opticaldistortion. In this case, the method further comprises: processing thepixel data of the first distorted sub-image to produce pixel datarepresenting a first planarized sub-image without conical opticaldistortion; processing the pixel data of the second distorted sub-imageto produce pixel data representing a second planarized sub-image withoutconical optical distortion; stitching the first and second planarizedsub-images together; and presenting a planarized image on a displaydevice, which planarized image includes at least the first and secondplanarized sub-images.

A further aspect of the subject matter disclosed in detail below is anapparatus for imaging a hole in a substrate, comprising: a multi-stageprobe placement head comprising a block assembly, a first stage which istranslatable relative to said block assembly along a first axis, asecond stage which is translatable relative to said block assembly alonga second axis orthogonal to said first axis, and a third stage which istranslatable relative to said block assembly along a third axisorthogonal to said first and second axes, said third stage beingtranslatably coupled to said second stage, and said second stage beingtranslatably coupled to said first stage; and an optical instrumentsupported by and depending from the third stage, wherein the opticalinstrument comprises: a housing coupled to and translatable with thethird stage; a light source disposed inside the housing; an image sensordisposed inside the housing; a conical mirror disposed outside thehousing and having a cone axis parallel to the first axis; a conicalmirror support structure that supports the conical mirror in a fixedposition relative to the housing; and an optical subassembly supportedby the housing and configured so that light from the light sourceimpinges on the conical mirror and is reflected radially outward by theconical mirror and light propagating radially inward and impinging onthe conical mirror is directed onto the image sensor.

A further aspect of the subject matter disclosed in detail below is asystem for imaging a hole in a substrate, comprising: an automatedapparatus configured to move an end effector by operation of motors, anoptical instrument mounted to the end effector, and an image processorconfigured to receive a conically optically distorted image acquired bythe optical instrument and then process pixel data of the conicallyoptically distorted image to produce pixel data representing aplanarized image without conical optical distortion. The opticalinstrument comprises: a housing coupled to the end effector; a lightsource disposed inside the housing; an image sensor disposed inside thehousing; a conical mirror disposed outside the housing and having a coneaxis parallel to the first axis; a conical mirror support structure thatsupports the conical mirror in a fixed position relative to the housing;and an optical subassembly supported by the housing and configured sothat light from the light source impinges on the conical mirror and isreflected radially outward by the conical mirror and light propagatingradially inward and impinging on the conical mirror is directed onto theimage sensor.

Other aspects of methods and apparatus for optical imaging and scanningof holes are disclosed below.

BRIEF DESCRIPTION OF THE DRAWINGS

The features, functions and advantages discussed in the precedingsection may be achieved independently in various embodiments or may becombined in yet other embodiments. Various embodiments will behereinafter described with reference to drawings for the purpose ofillustrating the above-described and other aspects. None of the diagramsbriefly described in this section are drawn to scale.

FIG. 1 is a diagram showing the principle of operation of an opticalinstrument suitable for imaging a hole using a conical mirror inaccordance with one embodiment.

FIG. 2 is a diagram showing a hole that will be illuminated whendownwardly axially propagating light is reflected radially outwardtoward a ring-shaped portion of the hole by a conical mirror.

FIG. 3 is a diagram showing a portion of FIG. 2 on a magnified scale.

FIG. 4 is a diagram depicting structural and functional aspects of anoptical instrument suitable for imaging a hole using a conical mirrorsupported by a central rod in accordance with one example embodiment.

FIG. 5 is a diagram depicting structural and functional aspects of anoptical instrument suitable for imaging a hole using a conical mirrorsupported by a glass tube in accordance with another example embodiment.

FIG. 6A is a diagram showing the geometric relationship of a circularcylindrical frame of reference for a hole and a conical mirror insertedin the hole and further showing a point on the hole surface and thecorresponding point on the image detected by an image sensor.

FIG. 6B is a diagram showing the location of an image point in a polarcoordinate system centered on the circular cylindrical frame ofreference for the hole.

FIG. 6C is a diagram showing a light ray which emanates from a point onthe hole surface, is reflected by a conical mirror and then producing animage point on an image sensor.

FIG. 7 is a diagram representing a three-dimensional view of an opticalinstrument suitable for imaging a hole using a conical mirror supportedby a central rod, which conical mirror is shown inside the hole.

FIG. 8 is a diagram representing a three-dimensional view of an opticalinstrument suitable for imaging a hole using a conical mirror supportedby a glass tube in accordance with a further example embodiment.

FIG. 9 is a diagram representing a side view of a crawler vehiclecarrying an optical instrument of the type depicted in FIG. 8.

FIG. 10 is a block diagram identifying some components of acomputer-controlled apparatus for optical imaging and scanning of holesin accordance with one embodiment.

FIG. 11 is a diagram representing an elevational view of the opticalinstrument of the type depicted in FIG. 8 mounted to a robot.

Reference will hereinafter be made to the drawings in which similarelements in different drawings bear the same reference numerals.

DETAILED DESCRIPTION

Illustrative embodiments of methods and apparatus for optical imagingand scanning of holes are described in some detail below. However, notall features of an actual implementation are described in thisspecification. A person skilled in the art will appreciate that in thedevelopment of any such actual embodiment, numerousimplementation-specific decisions must be made to achieve thedeveloper's specific goals, such as compliance with system-related andbusiness-related constraints, which will vary from one implementation toanother. Moreover, it will be appreciated that such a development effortmight be complex and time-consuming, but would nevertheless be a routineundertaking for those of ordinary skill in the art having the benefit ofthis disclosure.

Methods and apparatus for optical imaging and scanning of holesmachined, drilled or otherwise formed in a substrate made of compositeor metallic material will now be described in some detail for thepurpose of illustration. The method involves inserting an optical probehaving a conical mirror inside a hole, capturing a 360-degree sub-imageof a portion of the hole, and then sending the sub-image data to animage processor configured (e.g., programmed) to generate a planarizedsub-image without conical optical distortion. Multiple planarizedsub-images may be stitched together to form a complete planarized imageof the hole.

FIG. 1 is a diagram showing the principle of operation of an opticalinstrument 50 suitable for imaging a hole 6 in a substrate 2 made ofcomposite material (e.g., carbon fiber-reinforced plastic). The opticalinstrument 50 includes a microscope 10 having a housing part 16 a and alight source 18 inside a housing part 16 b. Other parts of the opticalinstrument housing are not shown in FIG. 1. An image sensor (not shownin FIG. 1) is disposed inside the housing part 16 a of microscope 10.The light source 18 is disposed inside the housing part 16 b. Inaccordance with some embodiments, the light source 18 is a monochromaticpoint light source.

The optical instrument 50 further includes a conical mirror 8 which issized to fit inside the hole 6. The conical mirror 8 is disposed outsidethe housing of the optical instrument 50 and has a cone axis. Theconical mirror is supported in a fixed position relative to the housingof the optical instrument 50 by means of a conical mirror supportstructure (not shown in FIG. 1). The conical mirror 8 has a geometricshape which is defined by revolving a line around the cone axis, whichline is disposed at an angle equal to 45 degrees relative to the coneaxis. In accordance with the implementation partially depicted in FIG.1, the conical mirror 8 has an apex 8 a and a base 8 c. However, itshould be appreciated that the conical mirror 8 may be truncated inalternative embodiments.

The optical instrument 50 partially depicted in FIG. 1 further includesan optical subassembly supported by the housing. The optical assemblyincludes an objective lens 12 supported by the housing part 16 a, a lens20 supported by the housing part 16 b, and a dichroic mirror 14 and amirror 22 supported by a housing part not shown. The dichroic mirror 14and a mirror 22 are both disposed at an angle of 45 degrees relative tothe optical axis of the objective lens 12 The optical subassembly isconfigured so that light (indicated by dashed arrows L1) from the lightsource 18 impinges on the conical mirror 8. The conical mirror 8reflects the impinging light radially outward toward a confrontingportion of hole 6. In addition, radially inwardly propagating lightreturning from hole 6 and impinging on the conical mirror 8 is reflectedtoward the objective lens 12 by the conical mirror 8. To avoid clutterin the drawing, FIG. 1 shows only one light ray L2 being returned to themicroscope 10.

In accordance with some embodiments, light L1 from light source 18source is directed axially (or nearly axially) toward the conical mirror8 by mirror 22 and dichroic mirror 14 during image acquisition. Morespecifically, light impinging on mirror 22 is reflected onto dichroicmirror 14. Dichroic mirror 14 then reflects light from the light sourceat an angle parallel to the optical axis of the microscope 10. Axiallypropagating light impinging on the conical mirror 8 is reflectedradially outward toward a confronting portion of hole 6. The apex 8 a ofconical mirror 8 is disposed along the optical axis of the microscope10. The conical mirror 8 receives axially (or nearly axially)propagating light and reflects the light radially outward to illuminatea confronting 360-degree ring-shaped portion of hole 6. Some of thatlight is scattered by the hole 6 back toward the conical mirror 8. Theconical mirror 8 then reflects that radially inwardly propagating lightaxially upward toward the dichroic mirror 14, which transmits the lightto the objective lens 12.

The dichroic mirror 14 allows transmission of light having a wavelengthin a certain range and reflects light having wavelengths outside thatrange. Dichroic mirror 14 may be designed to reflect light from lightsource 18 and to transmit light received from the conical mirror 8. Thedichroic mirror 14 is disposed at an angle of approximately 45 degreesrelative to the optical axis of the microscope 10. The 45-degreeorientation is preferred to maximize the effectiveness of the dichroicmirror and reflect incident light at a right angle. One example of adichroic mirror is a PYREX™ substrate having a borosilicate crown glasscoating. The specific wavelengths selected to be reflected or passed canbe controlled through careful selection of mirrors and coatings.Typically, after the ring-shaped hole portion 6 a absorbs the lightreflected radially outward by the conical mirror 8, the re-emission(scattering) of light happens at longer wavelengths. Therefore, theillumination must be chosen at shorter wavelength to have a betterdiscrimination of the scattered light back to the image sensor 30. Forexample, using a dichroic mirror that is set to transmit red light andreflect blue light, blue light from the light source 18 is reflected bythe dichroic mirror 14 toward the conical mirror 8. The blue lightilluminating the ring-shaped hole portion 6 a will cause the CFRPsurface to produce scattered red light (which has a wavelength longerthan the wavelength of blue light). The red light will be transmitted bythe dichroic mirror toward the image sensor 30 inside the microscope 10.

The image sensor 30 converts impinging photons into electrons andoutputs image data representing a full 360-degree sub-image of thering-shaped portion 6 a of hole 6 with conical optical distortion. In apost-processing step, the raw conical sub-image is transformed into aplanarized sub-image without conical optical distortion. The planarizedimage may then be further processed to evaluate the shape andconfiguration of hole 6. Thus, a system implementing the principle ofoperation depicted in FIG. 1 can be used to scan a hole in a depthwisedirection and produce a planarized image of the hole containinginformation characteristic of the particular hole. For example, theplanarized image may be processed to determine whether the shape andconfiguration (e.g. diameter, orientation and surface roughness) of thehole are within engineering tolerances

FIG. 2 is a diagram showing a hole 6 that will be illuminated whendownwardly axially propagating light impinges on and is reflectedradially outward toward a ring-shaped portion 6 a of hole 6 by thereflective surface of a conical mirror 8. In accordance with theembodiment depicted in FIG. 2, the conical mirror support structure thatsupports the conical mirror 8 in a fixed position relative to thehousing part 16 a is a central rod 24 having a linear axis and acircular cross section. In one proposed implementation, the axis of thecentral rod 24 is coaxial with the optical axis of the microscope 10.The center of X-Y rotational alignment is indicated by point 28 in FIG.2

In the example depicted in FIG. 2, a truncated portion 8 b of theconical mirror 8 is attached to one end of central rod 24. Themicroscope 10 further includes an image sensor 30 and an image-erectinglens 32 (hereinafter “second lens 32”) that is supported by the housingpart 16 a at a position between objective lens 12 and image sensor 30.The image sensor 30 may comprise a staring focal plane array, such as acharge coupled device (CCD) sensitive to visible or infraredwavelengths.

As previously described, the ring-shaped portion 6 a of hole 6 isilluminated by light which propagates axially into the hole, impinges onthe reflective surface of the conical mirror 8, and is then reflected bythat reflective surface radially outward. Some of the light reflectedonto the ring-shaped portion 6 a of hole 6 is reflected or scatteredback toward the reflective surface of the conical mirror 8, which inturn reflects returning light toward the objective lens 12. Theobjective lens 12 of the microscope 10 forms an image in a first imageplane that is perpendicular to the optical axis of the microscope 10.The second lens 32 receives light from the objective lens 12 and focusesthat light to form an image in a second image plane coincident with thephotoconductive surfaces of the image sensor 30. As a result, the imagesensor 30 (e.g., an array of photodetectors) acquires a raw conicalsub-image of the ring-shaped portion 6 a of hole 6.

FIG. 3 is a diagram showing a portion of FIG. 2 on a magnified scale.The inclined reflective surface of the conical mirror 8 is disposed at acone angle ω relative to the base 8 c. The height of the ring-shapedportion 6 a of hole 6 that is illuminated by light reflected by thereflective surface of conical mirror 8. In the case where the cone angleω is equal to 45 degrees, the height of the illuminated ring-shapedportion 6 a of hole 6 is equal to the distance separating the two lightrays L1 indicated in FIG. 3, which in this example represent theradially innermost and radially outermost light rays propagatingparallel to the cone axis and impinging on the reflective surface of theconical mirror 8. In an alternative example not shown in FIG. 3, theheight of the illuminated ring-shaped portion 6 a of hole 6 may equalthe height of the conical mirror (e.g., the distance between thetruncated portion 8 b and the base 8 c). The illuminating light has afocal plane F (indicated by a horizontal dashed line in FIG. 3)positioned at a distance below the base 8 c of the conical mirror 8.

In accordance with one proposed implementation, the conical mirror 8 isintermittently translated along the center line (Z-axis) of hole 6 by apredetermined distance and a respective raw conical sub-image iscaptured at each vertical position. In the time interval following eachmovement, the conical mirror 8 is stationary while the image sensor 30(see FIG. 2) acquires a raw conical sub-image. After one hole has beenfully inspected along the entire depth of the hole, the optical probe isremoved from that hole and then inserted into the next hole to beinspected. In this manner, a multiplicity of holes in a row of holes maybe inspected in succession.

FIG. 4 is a diagram depicting structural and functional aspects of anoptical instrument 50A suitable for imaging a hole 6 using a conicalmirror 8 supported by a central rod 24 with coaxial imaging and confocalillumination in accordance with one example embodiment. The axes of thecentral rod 24 and conical mirror 8 are coaxial with the optical axis ofthe microscope 10. The optical instrument 50A further includes a lightsource 18, a lens 20 and a small 45-degree mirror 42. The lens 20 isconfigured to focus the light from light source 18 onto the small45-degree mirror 42. An aperture plate 40 is disposed between the lens20 and the small 45-degree mirror 42. The small 45-degree mirror 42reflects the impinging light toward the objective lens 12 of themicroscope 10. The light from light source 18 is transmitted by theobjective lens 12 toward the opening 4 of hole 6 and onto the reflectivesurface of the conical mirror 8 for illuminating the ring-shaped portionof the hole 6 to be imaged.

In the example embodiment depicted in FIG. 4, the microscope 10 furtherincludes a second lens 32 and a charge coupled device image sensor 38(hereinafter “CCD image sensor 38”). (Although not shown in FIG. 4, theCCD image sensor 38 is supported by the housing part 16 a of themicroscope 10.) In a CCD image sensor, the photodetectors are p-dopedmetal-oxide-semiconductor capacitors. These capacitors are biased abovethe threshold for inversion when image acquisition begins, allowing theconversion of incoming photons into electron charges at thesemiconductor-oxide interface; the CCD is then used to read out thesecharges. The small 45-degree mirror 42 is sized to not obstruct lightpropagating from the objective lens 12 to the second lens 32. Forexample, the small 45-degree mirror 42 may be sized to fit within theshadow produced by the central rod 24. Thus, the light reflected upwardby the conical mirror 8 passes through the objective lens 12, around thesmall 45-degree mirror 42, and through the second lens 32 and thenimpinges on the CCD image sensor 38. The objective lens 12 has a firstimage plane located at point f. The second lens 32 has a second imageplane located at the CCD image sensor 38.

FIG. 5 is a diagram depicting structural and functional aspects of anoptical instrument 50B suitable for imaging a hole 6 using a conicalmirror 8 supported by a glass support tube 36 with coaxial illuminationand confocal imaging in accordance with another example embodiment. Theglass support tube 36 has respective anti-reflection coatings on itsinternal and external surfaces. The optical instrument 50B includes alight source 18, a lens 20, an aperture plate 40, a dichroic mirror 14and an objective lens 12. The light from the light source 18 propagatesthrough lens 20, aperture plate 40, dichroic mirror 14 and objectivelens 12 and into the hole 6. The light from light source 18 istransmitted onto the reflective surface of the conical mirror 8 forilluminating the ring-shaped portion of the hole 6 to be imaged.

In the example embodiment depicted in FIG. 5, the microscope 10 furtherincludes a second lens 32 and a CCD image sensor 38. The light reflectedupward by the conical mirror 8 passes through the objective lens 12 andis then reflected by the dichroic mirror 14 toward the second lens 32.Then the second lens 32 focuses the impinging light onto thephotoconductive surfaces of the CCD image sensor 38.

In accordance with one embodiment, the system for imaging a hole in asubstrate further comprises an image processor configured (e.g.,programmed) to receive a conically optically distorted image acquired bythe optical instrument and then process the pixel data of the conicallyoptically distorted image to produce pixel data representing aplanarized image without conical optical distortion. In one proposedimplementation, the image processor is programmed to execute aplanarization algorithm that comprises the following steps: convertingthe pixel data having image sensor coordinates to pixel data havingcylindrical coordinates corresponding to the hole surface and thenunrolling the cylindrical shell of the hole surface to a flattenedtwo-dimensional surface having X- and Y-axes (different than the X- andY-axes of the X-Y-Z coordinate system depicted in FIG. 2; the new Y-axisof the flattened two-dimensional coordinate system is parallel to theZ-axis of the X-Y-Z coordinate system). This transformation converts aflat two-dimensional Cartesian system (i.e., the image sensor pixelpositions) of the recorded reflected image of the hole surface from theconical mirror 8 to a new unfolded flat two-dimensional Cartesian systemthat represents the hole surface if it were flattened. The result isthat the conically optically distorted image is transformed to aplanarized image without conical optical distortion.

FIG. 6A is a diagram showing the geometric relationship of a circularcylindrical frame of reference 44 for hole and a conical mirror 8 havinga cone axis which is coaxial with the Z-axis of the hole. A point on thehole surface which has been imaged is represented by point P₀ in FIG.6A. The corresponding point on the image detected by the image sensor isrepresented by point P₁ in FIG. 6A and has coordinates in the frame ofreference of the image sensor equal to (im_(x), im_(y)). FIG. 6B is adiagram showing the location of an image point in a polar coordinatesystem centered on the circular cylindrical frame of reference 44 forthe hole.

FIG. 6C is a diagram showing a light ray which first propagates frompoint P0 radially inward along a path 46 perpendicular to the Z-axis, isreflected 90 degrees by the conical mirror, and then propagates upwardalong a path 48 until the light ray impinges on the image sensor, thusproducing the image point P₁. As best seen in FIG. 6C, the maximumradius of the conical mirror 8 is equal to R₀, while the distance fromthe Z-axis to the point where the light ray impinged on the conicalmirror 8 is equal to r. The angle between the X-axis and a vectorconnecting the origin of the X-Y coordinate system of the image sensorto the image point P₁ is indicated by θ in FIG. 6B.

The first step in the planarization algorithm is to convert the imagecoordinates (im_(x), im_(y)) and height h of point P1 to the polarcoordinates r and θ seen in FIG. 6B:

$r = {{{{R_{0} - h}\&}\mspace{14mu} \theta} = {{Tan}^{- 1}\left( \frac{{im}_{y}}{{im}_{x}} \right)}}$

The second step in the planarization algorithm is to flatten thecircular cylindrical frame of reference 44 and then convert the polarcoordinates r and θ to image coordinates (im_(x)′, im_(y)′) of point P₀in a planarized image, where im_(x)′ is equal to the arc length θR₀(shown in FIG. 6B) from the reference point O to the point P₀ andim_(y)′ is equal to the height h=R₋-r of point P₀ (shown in FIG. 6A):

${im}_{x}^{\prime} = {{\theta R_{0}} = {R_{0}{{Tan}^{- 1}\left( \frac{{im}_{y}}{{im}_{x}} \right)}}}$${im}_{y}^{\prime} = {{R_{0} - r} = {R_{0} - \sqrt{{im}_{x}^{2} + {im}_{y}^{2}}}}$

The above-described conic-to-planar transformation is performed on everyimage point acquired from a hole to produce a planarized image of thehole. That image is then displayed to technicians for the purpose ofenabling a visual inspection of the hole. The planarization algorithmdisclosed herein may be employed in conjunction with optical instrumentshaving different configurations, but sharing the common feature that theoptical probe to be inserted in each hole includes a conical mirror.

FIG. 7 is a diagram representing a three-dimensional view of an opticalinstrument 50C having a conical mirror 8 supported by a central rod 24inside a hole 6 in a substrate 2. The double-headed arrow indicates thatthe optical instrument 50C is movable vertically along a Z-axis which iscoaxial with the axis of the hole 6. The housing of the opticalinstrument 50C includes: (a) a housing part 16 a that houses componentsof the microscope 10; (b) a housing part 16 b that houses the lightsource 18; and a housing part 16 c that houses an optical subassemblythat includes a dichroic mirror 14 and a mirror 22 (indicated by adashed ellipses) both disposed at 45-degree angles relative to the axisof the objective lens 12. The objective lens 12 is supported by thehousing part 16 a. A lens 20 is supported by the housing part 16 b.Light from the light source 18 is transmitted by lens 20, reflected bymirror 22, reflected downward by dichroic mirror and then impinges onthe conical mirror 8. Returning light from the hole 6 is reflectedupward by the conical mirror 8, transmitted by the dichroic mirror 14and objective lens 12, and then impinges on the image sensor (not shownin FIG. 7) inside the microscope 10.

FIG. 8 is a diagram representing a three-dimensional view of an opticalinstrument 50D having a conical mirror 8 supported by a central glasstube 36 instead of a central rod 24. Other components depicted in FIG. 8have the same structure and functionality as like-numbered componentsdepicted in FIG. 7 and described in the immediately preceding paragraph.

FIG. 9 is a diagram representing a side view of a crawler vehicle 130having a multi-stage probe placement head 140 mounted on its forward endin accordance with one embodiment. The multi-stage probe placement head140 supports an optical instrument 50D, which can be used to image ahole 6 in a substrate 2 (such as a fuselage skin). Although only onehole 6 is shown, a multiplicity of holes 6 are typically arranged inrows. The optical instrument 50D is shown in a position where theoptical probe 26 is vertically aligned with a hole 6, e.g., an opticalaxis of the optical probe 26 is coaxial with a center line of the hole6. During an inspection procedure, the optical instrument 50D is placedat different depths inside the hole and is activated to capturerespective images at each depth.

The crawler vehicle 130 may take the form of a remotely operatedvacuum-enabled robot capable of holonomic motion along a surface whichis non-horizontal using wheels and suction devices (e.g., fans driven bymotors mounted on a frame of the crawler vehicle 130). In the embodimentdepicted in FIG. 9, only two wheels 122 a and 122 b of a set of fourwheels are visible; the suction devices are not shown. Rotation ofMecanum-type wheels driven by their respective motors (not shown)mounted on the frame of the crawler vehicle 130 enable holonomic motion.Holonomic motion, where turning and translating are decoupled, enablesscanning in any direction within the X-Y plane. The crawler vehicle 130may be steered for movement in an X-Y plane, with the X axis beingparallel to a row of holes 6 being inspected. Movement of the crawlervehicle 130 along a row of holes 6 is indicated by the longdouble-headed arrows labeled “Y TRANSLATION” in FIG. 9.

A video camera 90 is mounted on the crawler vehicle 130. The videocamera 90 can be oriented so that its field-of-view will include avolume of space under the multi-stage probe placement head 140. Thevideo camera 90 captures imaging data and sends that imaging data to acomputer (not shown in FIG. 9). The communication channel between thevideo camera 90 and the computer can be via an electrical cable orwireless. The computer will use the imaging feedback provided by thevideo camera 90 to control precision alignment of the optical instrument50D with the hole 6 to be inspected.

Still referring to FIG. 9, the multi-stage probe placement head 140comprises a block assembly 132 attached to the crawler vehicle 130, aZ-axis stage 142 translatably coupled to the block assembly 132, aX-axis stage 144 translatably coupled to the Z-axis stage 142, and aY-axis stage 146 translatably coupled to the X-axis stage 144. A mandrel148 is rotatably coupled to the Y-axis stage 146. The optical instrument50D is attached to the mandrel 148, i.e., the mandrel 148 and opticalinstrument 50D rotate in unison. The three stages of the probe placementhead 140 can be driven by motors for causing the optical instrument 50Dto move in the X, Y or Z directions respectively. The Z-axis stage 142is used to raise or lower the optical instrument 50D. The X-axis stage144 and Y-axis stage 146 provide precision motion for centering theoptical instrument 50D on the hole 6. The X, Y and Z axes are mutuallyorthogonal axes in the coordinate frame of reference of the crawlervehicle 130. In an ideal inspection scenario, the Z axis of the crawlervehicle 130 will be parallel to the center line of the hole 6 beinginspected. Multiple motions using smart servo or stepper motors (notshown in FIG. 9) with feedback control (based on imaging data acquiredby video camera 90) are used to precisely position the opticalinstrument 50D relative to the hole 6. When proper placement has beenrealized, the optical instrument 50D can then be lowered so that theoptical probe 26 is inserted into the hole 6. To enable rotation of theoptical instrument 50D (e.g., to avoid interference between opticalinstrument 50D and an obstacle), the mandrel 148 can be driven to rotateby a stepper motor (not shown in FIG. 9).

The system depicted in FIG. 9 is capable of inspecting holes 6 arrangedin rows, for example, on an aircraft fuselage, using the opticalinstrument 50D that is moved from hole to hole in succession. When theoptical instrument 50D is in proximity to the next hole 6, then thevideo camera 90 captures imaging data that is used to determine theposition of the optical instrument 50D relative to the hole 6. Then X-and Y-stage motors (not shown) on the multi-stage probe placement head140 can be operated to translate the optical instrument 50D in the Xand/or Y directions until the optical instrument 50D and hole 6 arealigned. Then the glass support tube 36 can be lowered to the startposition inside the hole 6 and the hole 6 can be scanned.

In the scenario depicted in FIG. 9, the optical instrument 50D is shownin a starting position in which a center line of the optical instrument50D is approximately coaxial with the center line of the hole 6. Thedouble-headed arrows in FIG. 9 indicate various movements which resultedin the scenario depicted in FIG. 9. First, the crawler vehicle was movedfrom a position where the optical instrument 50D was not in proximity tothe hole 6 to a position where the optical instrument 50D was inproximity to but not yet aligned with the hole 6 (this position is notshown in FIG. 9). In the scenario depicted, the crawler vehicle 130 wastranslated along the X axis, which is parallel to the row of holes towhich hole 6 belongs. When the hole 6 was within the field-of-view ofthe video camera 90, the crawler vehicle 130 was commanded to stop.While the crawler vehicle 130 and the optical instrument 50D werestationary, the video camera 90 was activated to acquire image datarepresenting the field-of-view, which included the opening 4 of hole 6.That image data was then processed by a computer (not shown in FIG. 9)using pattern recognition software to determine a location of a centerline of the hole 6 in a frame of reference of the crawler vehicle 130.The computer then used the location of the hole center line to determinea difference between the current position and the desired startingposition (shown in FIG. 9) of the optical instrument 50D in the frame ofreference of the crawler vehicle 130. Thereafter, while the crawlervehicle 130 was stationary, the optical instrument 50D was moved in theX and/or Y directions from its current position to the starting position(movement in the Y direction is indicated by a double-headed arrow inFIG. 9; movement in the X direction is not indicated). Then the opticalinstrument 50D was lowered from the start position into the hole 6 byactivating the motor (not shown) mechanically coupled to the Z-axisstage 142 (movement in the Z direction is indicated by a double-headedarrow in FIG. 9).

In accordance with the embodiment of the system depicted in FIG. 9, theX-, Y- and Z-axis stages may be translatably coupled by means ofrespective linear-motion bearings. These translatable stages may bemechanically coupled to respective stepper motors (see probe placementhead motors 54 in FIG. 10) by any suitable drive mechanism known in theart. For example, each stage could have a respective attached nut whichthreadably engages a respective lead screw which is driven to rotate bya respective stepper motor, thereby converting the rotation of the motoroutput shaft into translation of the stage.

FIG. 10 is a block diagram identifying some components of acomputer-controlled crawler vehicle 122 platform for optical imaging andscanning of holes in accordance with one embodiment. The crawler vehicle130 includes a video camera 90 mounted to a pan-tilt unit (not shown)and an optical instrument 50 mounted to the multi-stage probe placementhead 140 Both the pan-tilt unit and multi-stage probe placement head 140are mounted to the frame of the crawler vehicle 122. The opticalinstrument includes a microscope 10 and a light source 18 as previouslydescribed. The operations of the optical instrument 50 and the videocamera 90 are controlled by the computer system 72, which may beconfigured with programming stored in a non-transitory tangiblecomputer-readable storage medium (not shown).

The crawler vehicle 130 carries four wheel motors 124, whichrespectively drive rotation of four wheels 122. In the case wherein thecrawler vehicle is equipped with suction devices for vacuum adherence toinclined surfaces, the crawler vehicle may be further equipped with aplurality of EDF motors (not shown in the drawings) which drive rotationof a respective plurality of electric ducted fans. The probe placementhead 140 supports a plurality of probe placement head motors 54, threeof which drive translation of the optical instrument 50D along X, Y andZ axes respectively and one of which drives rotation of the opticalinstrument 50D about the Z axis. The pan-tilt unit includes pan-tiltmotors 76 which drive rotation of the video camera 90 about pan and tiltaxes respectively.

All of the motors received electrical power from power supplies viaswitches on a relay board (not shown in the drawings). The states ofthose switches are controlled by a computer system 72 onboard thecrawler vehicle 130. The computer system 72 may comprise ageneral-purpose computer programmed with motion control applicationsoftware comprising respective software modules for controlling thevarious stepper motors. The computer system 72 outputs control signalsto motor controllers 70 which selectively activate/deactivate each motorin accordance with those control signals.

In particular, the computer system 72 may be programmed to executeradiofrequency commands received from a ground-based computer system 80.Those radiofrequency commands are transmitted by a transceiver 82 whichis communicatively coupled to the ground-based computer system 80,received by a transceiver 74 onboard the crawler vehicle 122, convertedinto the proper digital format and then forwarded to the onboardcomputer system 72. The computer system 72 then controls: (a) themovements of the crawler vehicle 122 relative to the substrate; (b) themovements of the optical instrument 50 and video camera 90 relative tothe frame of the crawler vehicle 122; and (3) the acquisition of imagesby the optical instrument 50 and video camera 90. Thus, the operation ofthe equipment onboard the crawler vehicle 122 may be controlled by anoperator interacting with the ground-based computer system 80.

In particular, the probe placement head motor that drives displacementof the Z-axis stage 142 (hereinafter “Z-axis stage motor”) may becontrolled to place the glass support tube 36 at a vertical positionsuch that the apex or truncated portion of the conical mirror ispositioned at a first depth in the hole 6. While the conical mirror isstationary at the first depth, a first 360-degree image of the hole 6 isthen acquired. Then the Z-axis stage motor is controlled to place theglass support tube 36 at a vertical position such that the apex ortruncated portion of the conical mirror is positioned at a second depth(different than the first depth) in the hole 6. For example, thedistance separating the first and second depths may be equal to theheight of the optical mirror. While the conical mirror is stationary atthe second depth, a second 360-degree image of the hole 6 is thenacquired. These process steps may be repeated until the hole 6 has beenimaged along its entire depth. At the end of this process, the acquiredsub-images are planarized; then the planarized sub-images are stitchedtogether to provide one planarized image of the entire hole 6.

In accordance with one proposed implementation, the ground-basedcomputer system 80 includes a central processor 86 and an imageprocessor 88. The central processor 86 is configured (e.g., programmed)to send commands to the computer system 72 via transceiver 82 to controlmovements of the optical instrument 50 and video camera 90 and theacquisition of image data by the optical instrument 50 and video camera90. The central processor is further configured to receive image dataacquired by the optical instrument 50 and video camera 90 viatransceiver 82 and send that image data to the image processor 88. Theimage processor 88 is configured (e.g., programmed) to process the imagedata. In particular, the image processor 88 is programmed to execute analgorithm that converts conically optically distorted sub-imagesacquired by the optical instrument 50 into respective planarizedsub-images. The image processor 88 is further programmed to execute analgorithm that stitches the planarized sub-images together to form aplanarized image suitable for display on a display monitor 84. Thedisplay monitor 84 includes a display processor that may be configuredto display a planarized image of the hole 6 in one window and videoimages of the area of the substrate 2 surrounding the opening 4 inanother window.

FIG. 11 is a diagram representing an elevational view of the opticalinstrument 50D mounted to a robot 100. The optical instrument 50D isattached to the robot 100 by attaching a tool-side connector plate 60 toa connector 114 of the robot 100. While the optical probe 26 isstationary inside a hole, image data is sent to a data acquisitionsystem for processing. Typically, the robot 100 is automaticallycontrolled to move the optical probe 26 into alignment with a hole andthen into the hole.

The robot 100 has multi-axis movement capabilities and uses softwaresupport to generate a linear profile to be used for scanning a hole. Inparticular, the robot 100 shown in FIG. 11 comprises a robot base 102, acarousel 104, a rocker 106 (a.k.a. pivot arm), an extension arm 108, arobot hand 110, and a member 112 to which the connector 114 is attached.The robot base 102 and carousel 104 are rotatably coupled by a pivotalcoupling 116. The carousel 104 and rocker 106 are rotatably coupled by apivotal coupling 118. The rocker 106 and extension arm 108 are rotatablycoupled by a pivotal coupling 120. The rocker extension arm 108 androbot hand 110 are rotatably coupled by a pivotal couping 122. Thecombination of these components provides multiple degrees of freedom,which in turn allows the optical instrument 50D to be moved to differentlocations and in different directions. The robot 100 includes one ormore positional sensors (not shown) at, or otherwise associated with,each of the pivots that provide positional data (X, Y, and Z inthree-dimensional space) to the data acquisition system for accuratelylocating the optical instrument 50D. An example of a robot 100 thatcould be employed with the optical instruments disclosed herein is robotModel KR-150 manufactured by Kuka Roboter GmbH (Augsburg, Germany),although any robot or other manipulator capable of inserting an opticalinstrument ultrasonic inspection tool head and communicating with a dataacquisition system could be used.

The robot 100 is typically in communication with the data acquisitionsystem to process the image data acquired by the optical instrument 50Dand to display the processed data. In many cases, communicationscable(s) (not shown in FIG. 11) transmit data between the robot 100 andthe data acquisition system. In other embodiments, the data may betransmitted between the robot 100 and the data acquisition system viawireless communications. The robot 100 may be directly connected to thecomputer system 80 identified in FIG. 10, or indirectly connected, suchas via a network.

While methods and apparatus for optical imaging and scanning of holeshave been described with reference to various embodiments, it will beunderstood by those skilled in the art that various changes may be madeand equivalents may be substituted for elements thereof withoutdeparting from the teachings herein. In addition, many modifications maybe made to adapt the concepts and reductions to practice disclosedherein to a particular situation. Accordingly, it is intended that thesubject matter covered by the claims not be limited to the disclosedembodiments.

As used herein, the term “computer system” should be construed broadlyto encompass a system having at least one computer or processor, andwhich may have multiple computers or processors that communicate througha network or bus. As used in the preceding sentence, the terms“computer” and “processor” both refer to devices comprising a processingunit (e.g., a central processing unit) and some form of memory (i.e.,computer-readable medium) for storing a program which is readable by theprocessing unit.

The methods described herein may be encoded as executable instructionsembodied in a non-transitory tangible computer-readable storage medium,including, without limitation, a storage device and/or a memory device.Such instructions, when executed by a processor or computer, cause theprocessor or computer to perform at least a portion of the methodsdescribed herein.

The method claims set forth hereinafter should not be construed torequire that the steps recited therein be performed in alphabeticalorder (any alphabetical ordering in the claims is used solely for thepurpose of referencing previously recited steps) or in the order inwhich they are recited unless the claim language explicitly specifies orstates conditions indicating a particular order in which some or all ofthose steps are performed. Nor should the method claims be construed toexclude any portions of two or more steps being performed concurrentlyor alternatingly unless the claim language explicitly states a conditionthat precludes such an interpretation.

1. An optical instrument comprising: a housing; a light source disposedinside the housing; an image sensor disposed inside the housing; aconical mirror disposed outside the housing and having a cone axis; aconical mirror support structure that supports the conical mirror in afixed position relative to the housing; and an optical subassemblysupported by the housing and configured so that light from the lightsource impinges on the conical mirror and is reflected radially outwardby the conical mirror and light propagating radially inward andimpinging on the conical mirror is directed onto the image sensor. 2.The optical instrument as recited in claim 1, wherein the conical mirrorhas a geometric shape which is defined by revolving a line around thecone axis, which line is disposed at an angle equal to 45 degreesrelative to the cone axis.
 3. The optical instrument as recited in claim1, wherein: the conical mirror support structure comprises a centralpost; and the conical mirror is truncated and attached to one end of thecentral post.
 4. The optical instrument as recited in claim 3, whereinthe optical subassembly comprises a mirror and first and second lensesdisposed along an optical axis that is coaxial with the cone axis and athird lens disposed between the mirror and the light source, the mirrorbeing sized so that light propagating from the conical mirror to theimage sensor passes through the first lens, around the mirror andthrough the second lens.
 5. The optical instrument as recited in claim1, wherein: the conical mirror support structure comprises a circularcylindrical glass tube having a cylinder axis; and the conical mirror isdisposed inside the circular cylindrical glass tube so that the coneaxis is coaxial with the cylinder axis.
 6. The optical instrument asrecited in claim 1, wherein the optical subassembly comprises a dichroicmirror and first, second and third lenses which are arranged so thatlight propagating from the light source to the conical mirror passesthrough the third lens and is then reflected by the dichroic mirror, andlight propagating from the conical mirror to the image sensor passesthrough the dichroic mirror and then passes through the first and secondlenses.
 7. The optical instrument as recited in claim 1, wherein theoptical subassembly comprises a dichroic mirror and first, second andthird lenses which are arranged so that light propagating from the lightsource to the conical mirror passes through the third lens and thenthrough the dichroic mirror, and light propagating from the conicalmirror to the image sensor is reflected by the dichroic mirror and thenpasses through the first and second lenses.
 8. The optical instrument asrecited in claim 1, further comprising an aperture plate, wherein thethird lens is disposed between the aperture plate and the light source.9. A method for imaging a hole in a substrate, the method comprising:(a) placing a conical mirror into a hole with a cone axis coaxial with ahole center line and with an apex or truncated portion of the conicalmirror at a first depth which is less than a second depth of a base ofthe conical mirror; (b) illuminating the conical mirror with light thatis focused onto a focal plane inside the hole; (c) reflecting the lightrecited in step (b) radially outward toward the hole using the conicalmirror; (d) reflecting returning light axially upward toward the openingusing the conical mirror; (e) directing light reflected axially upwardby the conical mirror in step (d) onto an image sensor; and (f)converting light that impinges on the image sensor into electricalsignals that represent pixel data of a first distorted sub-image of afirst portion of the hole having conical optical distortion.
 10. Themethod as recited in claim 9, further comprising storing the pixel dataof the first distorted sub-image in a non-transitory tangiblecomputer-readable storage medium.
 11. The method as recited in claim 10,further comprising: retrieving the pixel data of the first distortedsub-image from the non-transitory tangible computer-readable storagemedium; and processing the pixel data of the first distorted sub-imageto produce pixel data representing a first planarized sub-image withoutconical optical distortion.
 12. The method as recited in claim 11,further comprising presenting the planarized first sub-image on adisplay device.
 13. The method as recited in claim 9, wherein the firstportion of the hole is an annular surface that extends from the firstdepth to the second depth.
 14. The method as recited in claim 9, whereinthe light reflected radially outward in step (c) encompasses an angle of360 degrees.
 15. The method as recited in claim 9, further comprising:(g) moving the conical mirror along the hole center line to a positionwhere the apex or truncated portion of the conical mirror is at a thirddepth which is closer to the second depth than to the first depth; (h)illuminating the conical mirror with light that is focused onto thefocal plane inside the hole; (i) reflecting the light recited in step(h) radially outward toward the hole using the conical mirror; (j)reflecting returning light of the light recited in step (i) axiallyupward toward the opening using the conical mirror; (k) directing lightreflected axially upward by the conical mirror in step (j) onto an imagesensor; and (l) converting light that impinges on the image sensor intoelectrical signals that represent pixel data of a second distortedsub-image of a second portion of the hole having conical opticaldistortion.
 16. The method as recited in claim 15, further comprising:processing the pixel data of the first distorted sub-image to producepixel data representing a first planarized sub-image without conicaloptical distortion; processing the pixel data of the second distortedsub-image to produce pixel data representing a second planarizedsub-image without conical optical distortion; stitching the first andsecond planarized sub-images together; and presenting a planarized imageon a display device, which planarized image includes at least the firstand second planarized sub-images.
 17. An apparatus for imaging a hole ina substrate, comprising: a multi-stage probe placement head comprising ablock assembly, a first stage which is translatable relative to saidblock assembly along a first axis, a second stage which is translatablerelative to said block assembly along a second axis orthogonal to saidfirst axis, and a third stage which is translatable relative to saidblock assembly along a third axis orthogonal to said first and secondaxes, said third stage being translatably coupled to said second stage,and said second stage being translatably coupled to said first stage;and an optical instrument supported by and depending from the thirdstage, wherein the optical instrument comprises: a housing coupled toand translatable with the third stage; a light source disposed insidethe housing; an image sensor disposed inside the housing; a conicalmirror disposed outside the housing and having a cone axis parallel tothe first axis; a conical mirror support structure that supports theconical mirror in a fixed position relative to the housing; and anoptical subassembly supported by the housing and configured so thatlight from the light source impinges on the conical mirror and isreflected radially outward by the conical mirror and light propagatingradially inward and impinging on the conical mirror is directed onto theimage sensor.
 18. The apparatus as recited in claim 17, wherein: theconical mirror support structure comprises a central post; and theconical mirror is truncated and attached to one end of the central post.19. The apparatus as recited in claim 17, wherein: the conical mirrorsupport structure comprises a circular cylindrical glass tube having acylinder axis; and the conical mirror is disposed inside the circularcylindrical glass tube so that the cone axis is coaxial with thecylinder axis.
 20. A system for imaging a hole in a substrate,comprising: an automated apparatus configured to move an end effector byoperation of motors; an optical instrument mounted to the end effector,and wherein the optical instrument comprises: a housing coupled to theend effector; a light source disposed inside the housing; an imagesensor disposed inside the housing; a conical mirror disposed outsidethe housing and having a cone axis parallel to the first axis; a conicalmirror support structure that supports the conical mirror in a fixedposition relative to the housing; and an optical subassembly supportedby the housing and configured so that light from the light sourceimpinges on the conical mirror and is reflected radially outward by theconical mirror and light propagating radially inward and impinging onthe conical mirror is directed onto the image sensor, and an imageprocessor configured to receive a conically optically distorted imageacquired by the optical instrument and then process pixel data of theconically optically distorted image to produce pixel data representing aplanarized image without conical optical distortion.